function v = piecelin(x,y,u)
%PIECELIN Piecewise linear interpolation.
% v = piecelin(x,y,u) finds piecewise linear L(x)
% with L(x(j)) = y(j) and returns v(k) = L(u(k)).
% First divided difference
delta = diff(y)./diff(x);
% Find subinterval indices k so that x(k) <= u < x(k+1)
n = length(x);
k = ones(size(u));
for j = 2:n-1
k(x(j) <= u) = j;
end
% Evaluate interpolant
s = u - x(k);
v = y(k) + s.*delta(k);